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Chapter 1 - INTRODUCTION

1.1 Photothermal Spectroscopy

Photothermal spectroscopy is a
group of high sensitivity methods used to measure optical
absorption and thermal characteristics of a sample. The basis of
photothermal spectroscopy is a photo-induced change in the
thermal state of the sample. Light energy absorbed and not
lost by subsequent emission results in sample heating. This
heating results in a temperature change as well as changes in
thermodynamic parameters of the sample which are related to
temperature. Measurement of the temperature, pressure, or density
changes that occur due to optical absorption are ultimately the
basis for the photothermal spectroscopic methods.

Ingle and Crouch (1988) classify
photothermal spectroscopy as one of several indirect methods for
optical absorption analysis. Indirect methods do not measure the
transmission of light used to excite the sample directly, but
rather measure an effect that optical absorption has on the
sample. The term indirect applies to the light measurement, not
to the optical absorbance. Photothermal spectroscopy is, in a
sense, a more direct measure of optical absorption than optical
transmission based spectroscopies. Sample heating is a direct
consequence of optical absorption and so photothermal
spectroscopy signals are directly dependent on light absorption.
Scattering and reflection losses do not produce photothermal
signals. Subsequently, photothermal spectroscopy more accurately
measures optical absorption in scattering solutions, in solids,
and at interfaces. This aspect makes it particularly attractive
for application to surface and solid absorption studies, and
studies in scattering media.

The indirect nature of the
measurement also results in photothermal spectroscopy being more
sensitive than optical absorption measured by transmission
methods. There are two reasons for this. First, photothermal
effects can amplify the measured optical signal. This
amplification is referred to as the enhancement factor
(Dovichi and Harris 1979, Mori, et al. 1982) and is the ratio of
the signal obtained using photothermal spectroscopy to that of
conventional transmission spectroscopy. Enhancement factors
depend on the thermal and optical properties of the sample, the
power or energy of the light source used to excite the sample,
and on the optical geometry used to excite the sample. Since the
optical excitation power or energy, and geometry is variable, the
enhancement can be made very large, even for samples with
relatively poor thermal and optical properties. In fact, the
problem with photothermal spectroscopy is not the absorption
detection limit. The problem is the detection of analyte
absorbance in the presence of a relatively large (10­5
cm­1) absorbance of the solvent. The second reason
photothermal spectroscopy is more sensitive than transmission is
that the precision of the measurement is inherently better than
that of the direct transmission method. The fundamental
limitation of conventional absorption spectroscopy, namely shot
noise, may be partially circumvented (Bialkowski, et al.
1992). Because of the increased fundamental signal to noise
ratios, the problem of being able to detect the analyte in the
presence of a relatively large background absorption should be
able to be overcome with perseverance.

The high sensitivity of the
photothermal spectroscopy methods has led to applications for
analysis of low absorbance samples. Dovichi (1987) reviewed the
literature regarding the use of photothermal spectroscopy for
chemical analysis. The magnitude of the photothermal spectroscopy
signal depends on the specific method used to detect the
photothermal effect and on the type of sample being analyzed.
There are many different reported detection limits and it is
difficult to specify an absolute lower limit of detection since
the method may be used to measure the background absorption of
the solvent itself. But it is safe to say that optical
absorbances of less than 10­6 can be detected with
optimized experimental designs. Subsequently, photothermal
spectroscopy is often characterized as a trace analysis method.
Concentration limit of detection measurements can be impressive.
Electronic transitions of strongly absorbing chromophores have
molar absorptivities exceeding 104M­1cm­1.
Using photothermal methods, concentrations lower than 10­10M of these strongly absorbing chromophores may be measured
in standard cuvettes. These limits of detection are slightly
higher than those obtained using laser excited fluorescence
spectroscopy and are 2-3 orders of magnitude better than that
obtained using conventional transmission spectroscopy. The low
molar absorption detection limits coupled with the fact that the
volume being probed can be very small results in extremely small
numbers of molecules being detected. The high absorbance
sensitivity of these methods has opened up new areas of trace
chemical analysis based on optical absorption spectroscopy.

Photothermal signals depend on
the thermodynamic and energy transfer properties of the sample.
Temperature changes resulting from optical absorption are
directly related to heat capacity and thermal conductivity. This
makes absolute sample absorption measurements difficult. The
thermal and optical properties of the sample must be known to
high accuracy, or the instrument response must be calibrated with
samples of known composition and absorbance. However, this
dependence on thermodynamic and energy transfer properties allows
for analysis of the thermal structure of materials. With
calibrated apparatuses, the static and dynamic thermal properties
of the sample can be measured. Photothermal spectroscopy has been
used to measure acoustic velocities, thermal diffusion
coefficients, sample temperatures, bulk sample flow rates,
specific heats, volume expansion coefficients, and heterogeneous
thermal conductivities in solids. In particular, a technique
called thermal wave imaging allows nondestructive material
inspection by measuring the rate of heat transfer in
heterogeneous materials.

Photothermal spectroscopy is
usually performed using laser light sources. There are two main
reasons for this. The first is the high spectral purity and
power. For an excitation of a sample with a given absorption
coefficient, the temperature change will be proportional to the
optical power, in the case of continuous excitation, or energy,
in the case of pulsed excitation. The photothermal spectroscopy
signal is generally proportional to the temperature change. Thus
the greater the power or energy, the greater the resulting
signal. Lasers can deliver high powers or pulse energies over
very narrow optical bandwidths thereby enhancing the photothermal
signals. The second reason is spatial coherence. The temperature
change is not only proportional to the optical power or energy,
but also is inversely proportional to the volume over which the
light is absorbed since heat capacity scales with the amount of
substance. The spatial coherence properties of laser sources
allow the light to be focused to small, diffraction limited,
volumes. The small volumes used in photothermal spectroscopy
enhances signal magnitudes, allows photothermal spectroscopy to
be used in small volume sample analysis, and allows for
microscopic analysis of heterogeneous materials.

1.2 Basic Processes in
Photothermal Spectroscopy

The basic processes responsible
for photothermal spectroscopy signal generation are shown in
Figure 1.1. Optical radiation, usually from a laser, is used to
excite a sample. The sample absorbs some of this radiation
resulting in an increase in the internal energy. The internal
energy is dispersed in two different modes of hydrodynamic
relaxation. The increased internal energy results in a
temperature change in the sample or the coupling fluid placed
next to the sample. This temperature change results in a change
in sample or coupling fluid density.

Figure 1.1 Processes involved in
photothermal spectroscopy. Absorption of radiation form the
excitation source followed by non-radiative excited state
relaxation results changes in the sample temperature, pressure,
and density. The density change is primarily responsible for the
refractive index change which can be probed by a variety of
methods.

If the photothermal induced
temperature change occurs faster than the time required for the
fluid to expand or in a few cases contract, then the rapid
temperature change will result in a pressure change. The pressure
perturbation will disperse in an acoustic wave. Once the pressure
has relaxed to the equilibrium pressure, a density change
proportional to the temperature will remain.

In either case there will be a
change in temperature induced by the absorption of optical
energy. This temperature change will in turn result in a density
change in the sample. In combination, temperature and density
changes affect other properties of the sample. Photothermal
spectroscopy is based on a measurement of these properties. In
particular, the sensitive photothermal methods are based on
measurement of the refractive index change that occurs with
changes in temperature and density of the sample.

Figure 1.2Several of the mechanisms for excited state relaxation
are illustrated. The main steps are optical interaction, energy
transfer, sample heating, and thermal effects. Radiative
relaxation, metastable state production, and photochemical
reaction may result in some sample heating. Energy transfer step
may result in fast or slow kinetic energy production.

There are three main areas that
must be considered when attempting to obtain a quantitative
description of the photothermal spectroscopy signal. The first is
a description of the optical absorption and excited state
relaxation processes. Optical excitation followed by excited
state relaxation results in sample heating. The rates and amounts
of excited state excitation and relaxation will control the rate
and magnitude of heat production. The energy transfer steps that
need be accounted for are shown in Figure 1.2. Energy can be
transferred to the sample by optical absorption and inelastic
scattering process such as Raman. Scattering is inefficient and
the amount of energy lost to sample is usually small enough to be
neglected. After absorption, the molecules are in an excited
state. Excited state relaxation transfers energy to the solvent
or sample matrix. Radiative relaxation does not result in
complete loss of the absorbed energy to the sample. Some of the
energy is lost in the form of the radiated light. Thermal
relaxation transfers the energy to the sample matrix and results
in sample heating. Excited species may also form long lived
metastable states that trap energy and prevent further optical
absorption. This will result in a delayed heating of the sample.
The excited state species may also participate in photochemical
reactions. Photochemical reaction can produce heat but also
produce new chemical species which alter the thermal and optical
characteristics of the sample.

These relaxation processes may
all produce excess energy in the form of heat. The heat increases
the internal energy of the sample. The sample will respond to
this increased energy. The second area is that of the
hydrodynamic relaxation. After optical heating, the sample is not
at thermal equilibrium with itself or with the surrounding
environment during a measurement. Heat generated by the optical
excitation and relaxation processes will result in thermal
gradients between the excited sample and the surroundings. The
thermal gradients result in heat transport. Heat is transferred
within the sample in a fashion such as to move toward thermal
equilibrium. Hydrodynamic relaxation produces changes in the
temperature, pressure, and density of the sample.

The third area is that of the
signal generation process. Photothermal spectroscopy signals are
based on changes in sample temperature or related thermodynamic
properties of the sample. These are usually monitored through the
refractive index of the sample or a thermal coupling fluid placed
in contact with the sample. Several properties may affect the
refractive index of the medium. The most common is the density.
However the refractive index may also change with temperature,
population in optically excited states, and with chemical
composition if photochemical reaction occurs. There are a variety
of instrumental methods used to probe the changes in the sample's
refractive index. Other instrumental methods used for
photothermal spectroscopy directly probe the temperature or
related thermodynamic properties, but the most sensitive methods
probe the spatial or temporal gradients of these properties.

A schematic diagram illustrating
the main components to apparatuses used for photothermal
spectroscopy is shown in Figure 1.3. Most apparatuses consist of
six main components;

sample

light used for sample
excitation

light used to monitor
refractive index perturbations

a mask, aperture, or other
form of spatial filter for the probe light

an optical detector used to
detect the optically filtered probe light

electronic signal processing
equipment

The excitation light heats the
sample. The probe light monitors changes in the refractive index
of the sample resulting from heating. The spatial and propagation
characteristics of the probe light will be altered by the
refractive index. The spatial filter selects those components of
the altered probe light that change with the samples' refractive
index. The optical detector monitors changes in the probe light
power past the spatial filter. In some apparatuses, a spatial
filter and a single channel detector are combined using an image
detector. Signals generated by the photodetector are processed to
enhance the signal to noise ratio.

In addition, an apparatus may
also be equipped with detectors to monitor the excitation and
probe light power, a thermostatic sample holder, and optical
spatial filters to control the spatial profiles of the excitation
and probe light. This additional equipment is used to control the
experiment environment and to measure the optical power required
to accurately quantify changes that occur in the sample. These
components are necessary when the data must be used to determine
absolute absorption of the sample.

In theory, the photothermal
spectroscopy signal can be accurately calculated based on
knowledge of the experimental apparatus, the parameters that
characterize light propagation, and the optical parameters of the
sample. The following items must all be accounted for in the
calculations;

determine the optical
absorption resulting in sample heating

determine the rate of heat
production

determine the temporal and
spatial temperature and density change

relate the refractive index
change to the temperature or density change using the
thermal-optical parameters of the sample

calculate the strength of
the optical element formed from the spatial-dependent
refractive index change

calculate the optical and
electronic signal resulting from passage of light through
apertures or using specialized detectors.

1.3 Photothermal spectroscopy
methods

There are a variety of methods
used to monitor the thermal state of the analytical sample
(Harris 1986, Tam 1986, Dovichi 1987, Tam 1989). Direct
calorimetric or thermometric methods use temperature transducers
to measure analytical sample temperature. Pressure transducers
areused to monitor the pressure wave associated with rapid sample
heating. Photothermal interferometry, photothermal deflection
spectroscopy, photothermal lensing spectroscopy, also known as
thermal lens spectroscopy, photothermal diffraction spectroscopy,
and methods based on sample reflection changes are all based on
monitoring refractive index changes associated with sample
heating. Infrared detectors can be used to monitor changes in the
samples infrared emission associated with heating. Each of these
methods are based on a measurement of temperature change
associated with increasing the energy of the analytical sample.

Photothermal methods have been
reported by individuals working in several areas of science and
technology. Subsequently, there are several names that the
particular methods are known by. The temperature changes
resulting from the photothermal effect can be detected using a
variety of methods. These methods are summarized in Table 1.1.
Temperature can be directly measured using thermocouples,
thermistors, or pyroelectric devices in the method of photothermal
calorimetry. Temperature changes can also be indirectly
measured using methods which monitor infrared emission since the
thermal infrared emission is related to sample temperature. The
method of thermal emission or photothermal radiometry
of infrared radiation can be used to monitor relatively large
temperature changes that occur as a consequence of optical
absorption. Although not very sensitive, this method has great
potential for application in nondestructive materials analysis
and testing. Using infrared sensitive cameras, it can be used for
imaging the thermal properties of large samples.

Two other temperature dependent
thermodynamic parameters that are commonly exploited in
photothermal spectroscopy are pressure and density. The pressure
changes that occur upon periodic or pulsed sample heating can be
detected by using a microphone or other pressure transducer to
monitor the acoustic wave. The method of optoacoustic or photoacoustic
spectroscopy is based on the measurement of this pressure
wave.

Although produced by the same
photothermal effects, photoacoustic, infrared radiometry, and
photothermal spectroscopies are typically treated as separate
methods. Photothermal spectroscopy refers to methods that monitor
the temperature dependent refractive index changes, usually with
a probe laser. Nonetheless, it is apparent from hydrodynamic
relaxation that the photoacoustics cannot be avoided in a
treatment of photothermal spectroscopy. The photoacoustic
pressure wave generated by the photothermal effect is observed in
photothermal spectroscopy and the rate of sample relaxation is
controlled by the rate at which the sample can approach isobaric
conditions. Moreover, infrared emission is another method of
thermal heat transfer that should at least be quantified in terms
of the effect that it may have on the photothermal signal
magnitude. All of these effects should be considered in a
comprehensive treatment of the photothermal effect.

Under steady-state, isobaric
conditions, the density is related to the temperature through the
volume expansion coefficient. Temperature dependent density
changes are difficult to measure directly. But density changes
can affect samples in several different ways. In solid samples,
the density change alter physical dimensions at sample surfaces.
Sample dimension changes give rise to two optical methods for
monitoring the temperature change based on surface deformation. A
homogeneous deformation (expansion or contraction) displaces the
surface of the sample. Interferometry can be used on reflective
samples. Since small displacements, on the order of a few
parts-per-million of the wavelength of probe beam light, can be
measured using interferometry, this method may be used for
sensitive measurement solid sample absorption. Spatially
heterogeneous expansion (or contraction) can also cause the
surface angle to change. A probe beam reflected from the surface
will change angle when heterogeneous expansion occurs.
Measurement of the probe beam angle gives rise to the method of photothermal
surface deflection spectroscopy.

The majority of studies
addressing the use of photothermal spectroscopy for chemical
analysis have been based on refractive index measurements. In
transparent samples, the temperature dependent refractive index
of the sample itself is probed. For opaque or scattering
surfaces, temperature dependent changes in the refractive index
of fluid that couples heat out of a solid sample are measured.
There are several methods used to detect the resulting refractive
index change. Several of these are shown in Figure 1.4.
Publications in photothermal spectroscopy come from researchers
working in the fields of analytical and physical chemistry,
physics, and optical engineering. Subsequently there is a wide
range of nomenclature used to describe methods for refractive
index change detection in the photothermal spectroscopy
literature. But all of these methods rely on a few basic
principles of light propagation, namely, optical pathlength
changes, diffraction, and refraction. Light refraction can result
in a direction change and/or focussing.

Figure 1.4 Four methods
used for photothermal spectroscopy. Interferometry directly
measures the refractive index. Deflection measures the gradient.
Photothermal lens spectroscopy is based on beam focusing or
defocusing. Diffraction methods measure the power of a beam
diffracted by the periodic index.

The optical pathlength changes
that occur due to the photothermal induced refractive index
change can be measured with interferometry. Using interferometry,
the phase of monochromatic light passing through the heated
sample, relative to the phase passing through the reference arm,
results in a change in power at a photoelectric detector. There
are several different interferometry schemes that can be used to
detect changes in the optical pathlength induced by the
photothermal effect. These methods may all be classified as being
photothermal interferometry.

Spatial gradients in refractive
index result in a direction change in the propagation of a ray of
light. Thus light will exit a medium with a refractive index
gradient at an angle relative to the incident ray. This bending
of light path is commonly called photothermal deflection
spectroscopy.

Spatial dependent refractive
index profiles can also result in focusing or defocusing of
light. This occurs when the refractive index profiles are curved.
Thus the thermally perturbed sample can act as a lens. Light
transmitted through an aperture placed beyond the photothermal
lens will vary with the strength of the lens. Photothermal
methods based on measurement of the strength of this lens are
called photothermal lensing spectroscopy. Some
experimental apparatuses measure a signal that is due to the
combined effects of deflection and lensing. These may be
generally classified as photothermal refraction spectroscopy
methods.

Lastly, a periodic spatial
refractive index modulation results in a volume phase diffraction
grating. The grating will diffract light at an angle that meets
requirements from Bragg's Law. The amount of light diffracted is
proportional to the refractive index change. The diffracted light
is measured with a photoelectric detector. Methods used to
measure spectroscopic signals based on volume phase diffraction
gratings formed by the photothermal effects are called photothermal
diffraction spectroscopy.

The key to the success of
sensitive photothermal apparatuses lies in measurement of a
thermal change and not the thermal state itself. Although
apparatuses could directly or indirectly measure the
thermodynamic parameters such as temperature, pressure, density,
and energy state, the limiting absorption that could be measured
would be imposed by thermodynamic fluctuations. Sensitive
photothermal spectroscopy methods circumvent direct measurements
by measuring refractive index changes due to a non-equilibrium
change in the energy of the sample. The change occurs in both
space and time. Photothermal spectroscopy methods measure some
effect that the spatially or temporally dependent refractive
index change has on the propagation characteristics of light used
to monitor the refractive index.

Each of these apparatuses detect
the change in refractive index that accompanies optical
absorption. Photodetectors are used to monitor probe power
changes. These power signals are time dependent. The analytical
signal is usually related to the change in detected power
relative to the incident power of the probe. There are three main
types of time dependence that analytical signals can have. These
in turn depend on the temporal character of the excitation
source. The main excitation and detection schemes are given in
Table 1.2

Table 1.2 Main
sample excitation schemes used in photothermal spectroscopy

Pulsed excitation sources produce
transient signals. These signals are a maximum immediately
following sample excitation and decay as the sample approached
equilibrium through thermal diffusion. The transient signals last
from a few microseconds in the gas phase to several milliseconds
in condensed phases. The time duration is inversely proportional
to the thermal conductivity of the media since thermal diffusion
or conduction removes energy from the sample and more
importantly, distributes the energy throughout the sample.
Photothermal lens, deflection, and diffraction apparatuses
respond to spatial variations in the refractive index. Thus
homogeneous distribution of energy throughout the sample does not
result in a signal. Interferometry measurements may be able to
detect the refractive index change after thermal diffusion has
distributed the energy. However, environmental thermal stability
is usually not good enough to allow this. Sensitive
interferometry apparatuses rely on the detection of a temporal
change in refractive index.

Continuous excitation produces
signals that are initially small but increase in magnitude as the
irradiation time progresses. Initially, thermal diffusion removes
heat slower than the heat produced by optical excitation. The
Fourier law of heat diffusion states that the heat flux, jH,
is proportional to the temperature gradient

The proportionality constant is
the thermal conductivity. As the sample absorbs radiation and
converts the energy to heat, the temperature gradient increases.
When the radiative heating flux equals the energy flux due to
thermal conduction, a steady-state spatially-dependent
temperature change is attained. Thus the photothermal signals
eventually reach a steady-state value. The signals develop over
the course of from milliseconds to seconds, the time required to
attain the steady-state value being proportional to the thermal
conductivity.

For analytical, e.g.
concentration, measurements, both pulsed and continuous
excitation requires estimation of the signal magnitude. Signal
magnitudes are directly proportional to the sample absorbance in
a first order approximation. Signal magnitudes can be measured
directly, for example using an oscilloscope or ammeter, or the
signal transient can be recorded and subsequently processed to
enhance measurement precision.

Excitation sources may also be
modulated. Chopped or oscillatory excitation produces oscillating
signals. The resulting signals can be processed using band pass
filters or lock-in amplifiers. The magnitudes of the oscillating
signals depend on sample absorbance, the frequency of excitation,
and thermal conductivity of the medium. With modulated
excitation, signal magnitudes are proportional to sample
absorbance but decrease with increasing frequency. In addition to
the signal amplitude information, phase-sensitive lock-in
analyzers also produce signal-to-excitation phase-shift
information. The frequency dependent phase-shift information is
essentially equivalent to that contained in the time-dependent
signal transients obtained using pulsed excitation.

1.4 Application of
Photothermal Spectroscopy

There have been many applications
of photothermal methods for chemical and material analysis. Tam
(1983, 1986, 1989) is perhaps primarily responsible for sorting
through the vast amount of literature and characterizing the
applications of these methods. Many of these applications are
covered in the book edited by Sell (1989). These applications
fall under four main categories.

Photothermal spectroscopy:
the signal magnitude is measured as a function of
wavelength in this application. The photothermal signal
is proportional to the absorbed light. So the spectrum is
technically an excitation spectrum. The resulting
excitation spectrum can be an accurate measure of the
absorption spectrum if the thermal quantum yield and
fraction of light transmitted to the absorber do not
change with wavelength. This technique has found
widespread use for solid sample analysis where incoherent
excitation light sources can be used. Applications to
liquid and gas sample analysis has been limited because
of the difficulties encountered when attempting to scan
the wavelengths of lasers while keeping them focused at
a particular position.

Photothermal detection:
is similar to photothermal spectroscopy only a single
wavelength source is used to excite the sample. The
signal magnitude can be related to sample absorbance or
analyte concentration. Samples must be prepared and
separated so that there is no interference absorption and
so that the sample matrix is the same for all measured
samples. The main application is for trace analysis.
Although not restricted to coherent sources, this
application is normally performed using laser excitation
sources to enhance the limits of detection. The
application is also suited for effluent detection in
chromatography. The spatial coherence of lasers allows
the use of small volume detection cells or on-column
detection.

Photothermal monitoring
of excitation and relaxation process: in this
application the signal magnitude is measured as a
function of time or excitation irradiance. The time
dependent data is used to deduce photophysical and
photochemical parameters such as excited state lifetimes,
enthalpies of formation, lifetimes of metastable states,
and thermalization times. The excitation irradiance
dependent data can be used to calculate multiphoton
absorption cross-sections and parameters relating to
optical saturation and bleaching.

Photothermal probing of
the physical properties: many of the physical
properties of a sample can be determined using
photothermal methods. Photothermal methods have been used
to measure temperature, thermal diffusivities, sound
velocity, bulk flow velocities, surface thickness, and
specific heats. In homogeneous samples, the full
photothermal transient is typically analyzed in order to
obtain this information. However, some of these
parameters can be determined by measuring signal
magnitudes, signal decay times, and signal onset times
for carefully designed experiments. Thermal properties of
heterogeneous samples can be obtained by raster scanning
the optical excitation source over the sample surface. In
this case the signal magnitude and phase is measured as a
function of spatial coordinate.

1.5 Illustrative history of
photothermal spectroscopy1.5.1 Nature of the photothermal
effect

Most of us observe the
photothermal effect in our lives. On the beach, sand is too hot
to walk on with bare feet in midday summer. This is because the
sand absorbs sun's radiation and converts this energy to heat.
The added heat results in a temperature increase because of the
finite heat capacity of the sand. When the heat is generated
faster than it can be dissipated by radiative or diffusive
mechanisms, the temperature of the sand increases. However, the
rate of heat dissipation increases with the temperature
difference between the surface sand, and soil below or air above
it. Under constant illumination conditions, the sand reaches an
equilibrium temperature wherein the rate of heat generated by the
photothermal effect is balanced by the rate at which the heat is
dissipated. Another way we utilize the photothermal effect is to
warm ourselves by the radiation of a campfire. Here, our skin is
the absorber and the campfire is the source of the infrared
radiation.

A concrete example of the
photothermal effect, which is also the basis for a photothermal
spectroscopy method, is the shimmering surface or optical mirage
effect. This effect is illustrated in Figure 1.5 . A hot highway
sometimes looks like a reflective surface. It appears as if it
were a puddle of water. We come to understand that the apparently
shiny surface is not due to reflection. It is just a mirage. In
fact, the mirage effect is one of the photothermal effects that
have been exploited for chemical and materials analysis.
Radiation from the sun is absorbed by the concrete or asphalt
resulting in surface heating. The hot surface transfers energy to
the air above the surface. A temperature gradient develops
between the air near the surface and the bulk air above. Air
expands when it is heated. The density of the air at the surface
is less than that in the bulk. The decreased density results in a
decreased refractive index. Since the speed of light is faster in
the low refractive index media, light incident at an acute
tangent angle is refracted upward. An observer looking at the
surface at an acute tangent angle does not see the surface but
rather sees the rays coming from the sky above the surface.

Figure 1.5 An early photothermal
deflection apparatus for measuring absorbance of the earths
surface. Since the signal depends of meteorological and solar
conditions, this measurement it is difficult to obtain accurate
numbers using the human detector.

It is likely that our
predecessors had a working knowledge of the photothermal effect
long before they could apply more abstract concepts such as
optical transmission, color, and other factors leading to modern
theories of spectroscopy. But although photothermal effects may
have been recognized in the prehistoric past, it took an
understanding of the photothermal process to apply the
photothermal effect for spectrochemical measurements. Much of
what is now known about photothermal spectroscopy has been
developed over the past century. Many of the advances came about
as a result of the developments in laser technology about 25
years ago. Other advances were made simple by the recognition and
understanding of what is now called the photothermal effect.

1.5.2 Photoacoustic
spectroscopy

The oldest technical application
of the photothermal effect is believed to be the communication
device, the photophone, invented by Bell (1880, 1881). Bell found
that audible sound could be heard coming from a tube filled with
various materials when the light shining on the transparent tube
was modulated. The sound was loud when the tube was filled with
radiation absorbing gases or solids, and weak when filled with a
liquid. The operational principles are now well understood.
Modulation of the light impinging on an absorbing substance will
produce a similar modulation in temperature through the
photothermal effect. In a gas of restricted volume, temperature
modulation produces a pressure modulation. The periodic pressure
modulation is an acoustic signal.

Some time later Viengerov (1938)
used the photoacoustic effect to study light absorption in gases
and obtained quantitative estimates of concentration in gas
mixtures based on signal magnitudes. This may have been the first
use of photoacoustic spectroscopy. Sensitive chemical measurement
applications followed the work of Kerr and Atwood (1968) who used
a laser to excite the samples. More interest in the method was
generated when Kreuzer (1971) demonstrated part-per-billion (ppb)
detection sensitivities of methane in nitrogen using a 3.39 :m
helium-neon laser excitation source, and later (Kreuzer 1972)
sub-ppb of ammonia and other gases using infrared CO and CO2
lasers. These high sensitivity measurements were possible because
of the laser source used for excitation. Large photoacoustic
spectroscopy signals resulted from the high spectral brightness
and the spatial coherence of the lasers used for sample
excitation. The photoacoustic measurement methods came at about
the same time as the recognition that trace species could have a
major impact on the environment.

In the time since the first
chemical measurements by Viengerov (1938), the theory and
practice has been developed to a high degree. The theories for
sound generation, propagation, and interaction with matter were
developed though the mid-20th century (Landau and Lifshitz 1959,
Herzfeld and Litovitz 1959) and acoustics were applied to
physical chemical analysis. The theories are complex and exact
solutions for sample excitation and signal generation are often
difficult to interpret and verify. Nonetheless, the principles of
photoacoustic spectroscopy are now commonly understood and
photoacoustic spectroscopy is being applied to a wide range of
analysis problems.

The essential components for an
apparatus used for photoacoustic spectroscopy is shown in Figure
1.6. The light source, either pulsed or modulated, periodically
heats the sample by the photothermal effect. Periodic sample
heating followed by expansion causes a periodic pressure wave
which is detected with the pressure transducer. The pressure
transducer signal is proportional to the amplitude of the
pressure wave. Consider a sample that has a low enough absorption
coefficient that the transmission can be approximated by

where T(l) is the
optical pathlength, l (m), dependent transmission, and a (m­1)
is the absorption coefficient. The amount of energy absorbed from
a laser source with an optical energy of Q (J) is Q[1-T(l)].
Qal. If the quantum yield for heat
production is unity, all the absorbed optical energy is converted
into heat. The peak pressure change, dPacoustic (Pa),
is proportional to (Lai and Young 1982, Tam 1986)

where c (m s­1)
is the sound velocity, b (K­1) is the volume expansion
coefficient, r (m) is the radial distance between the
transducer and the source, CP (J kg­1
K­1) is the specific heat, Q (J) is the pulse
energy, and the pressure perturbation time, t (s), is the
root-mean-square average of the relaxation times and the pulse or
modulation width. Relaxation times may include contributions from
the excited state relaxation time and the acoustic relaxation
time

where ta (s) is the acoustic
relaxation time, and w (m) is the radius of the beam used
for sample excitation. The acoustic relaxation time is that
required for the heated sample to expand.

The important points to be
deduced from the acoustic pressure equation are;

the signal scales as the aQ
product

the signal falls off as the
pressure transducer is moved away form the excited region
as r­2

the signal is inversely
proportional to the pressure perturbation time, favoring
short pulse excitation and small beam waists

the signal magnitude is
proportional to the thermodynamic properties of the
sample through the (bc2/CP)
term

In general, b is much
smaller for liquids and solids than it is for gases. Not only
does this explain the early observations of Bell (1881) but also
explains why direct photoacoustic spectroscopy is most sensitive
for gas sample analysis.

<Figure
1.6>

Figure 1.6 Schematic of a
photoacoustic spectrometer based on direct acoustic wave
detection. Chopped (a) or pulsed (b) sample excitation results in
acoustic pressure wave generation. The signal is detected with a
piezoelectric pressure transducer and processed with either a
lock-in or sampling (boxcar) amplifier. (Figure from Tam, 1986)

The spectra of solid or liquid
samples can be measured by directly coupling the acoustic wave to
a transducer or by coupling the heat generated at the surface to
a gas "coupling fluid." This principle was used in
Bell's original photophone but wasn't rediscovered until Parker
(1973) noticed that optical energy absorbed by the gas sample
cell windows would transfer heat to a gas thereby causing a
significant photoacoustic signal. This effect was developed by
Rosencwaig (1977, 1980) and is now commonly used for obtaining
spectra of strongly absorbing solids and liquids. A modern
version of a device for photoacoustic spectroscopy of condensed
samples is shown in Figure 1.7. A solid or liquid sample is
placed in the sealed photoacoustic cell. The excitation source is
absorbed at or near the surface. Absorbed radiation is randomized
increasing the surface temperature. The heated surface heats the
gas causing it to expand. Periodic heating of the surface creates
an acoustic wave that is monitored with the sound transducer.

<Figure
1.7>

Figure 1.7 Schematic of an
indirect photoacoustic spectrometer based on chopped excitation.
The thermal perturbation generated in the sample is coupled to
the fluid, usually a gas, an sensed with the microphone pressure
transducer. The microphone signal is then processed with a
lock-in amplifier to enhance the signal. (Figure from Tam, 1986).

There have been scores of
publications on the uses of photoacoustic spectroscopy for
chemical and material analysis. Absorption detection limits (a) are about 10­10
cm­1 for gases (Patel, et al. 1977) and 10­6
cm­1 for liquids (Beitz, et al. 1990). These
are very close to the theoretical detection limits (Zharov and
Letokhov 1985). Many review articles and books have been written
on this method. Some of the more recent reviews of general
applications are Tam (1983, 1986), Hutchins and Tam (1986). Patel
and Tam (1981) reviewed applications of photoacoustic
spectroscopy for condensed matter. Betteridge and Meylor (1984)
have reviewed the applications of photoacoustic spectroscopy in
chemical analysis. Zharov (1986) reviewed photoacoustic
applications to chromatography. Meyer and Sigrist (1990) have
reviewed applications to gas analysis. General books on
photoacoustic spectroscopy include those of Pao (1977),
Rosencwaig (1980), and Zharov and Letokhov (1986). Mandelis
(1987) has edited a book on application of photoacoustic and
photothermal spectroscopy methods for semiconductor analysis.
Hess (1989a and 1989b) has edited a books regarding the
application of photoacoustic and photothermal spectroscopy
methods for gas and surface analysis. Nyquist, et al.
(1990) and Putzig, et al. (1992) have reviewed
photoacoustic and photothermal spectroscopies in their ANALYTICAL CHEMISTRYFundamental
Reviews of infrared analysis. Kitamori and Sawada (1991) have
discussed unconventional applications in their review.

1.5.3 Photothermal lens
spectroscopy

The first photothermal
spectroscopic method to be applied for sensitive chemical
analysis was photothermal lens spectroscopy. The photothermal
lens effect was discovered when Gordon, et al. (1964,
1965) observed transient power and beam divergence changes in the
output of a helium-neon laser after placing
"transparent" samples in the laser cavity. Their
apparatus, shown in Figure 1.8, was originally intended to be
used as a high irradiance source for Raman spectroscopy. They
observed the photothermal lens effect when pure organic liquids
and solids, glass and lucite, were placed in the laser cavity. A
theory describing the effect was developed to account for their
observations. This theory was an accurate description of the
physics of thermal lens formation and signal generation, and is
essentially the same as that used to this day (Whinnery 1974).
The photothermal lens results from optical absorption and heating
of the sample in regions localized to the extent of the
excitation source. The lens is created through the temperature
dependence of the sample refractive index. The lens usually has a
negative focal length since most materials expand upon heating
and the refractive index is proportional to the density. This
negative lens causes beam divergence and the signal is detected
as a time dependent decrease in power at the center of the beam.

<Figure
1.8>

Figure 1.8 First
photothermal lens apparatus. The sample was placed in the cavity
of the laser. Irises were used to restrict the laser to single,
TEM00, mode operation. Detectors were used to measure
the laser power, and the laser output both with and without an
external pinhole. (Figure 1 from Gordon, et al. 1985)

Laser output power transients for
the first apparatus are shown in Figure 1.9. Although the theory
was accurate, these transients were difficult to interpret. The
transients arose due to the interaction between the intracavity
beam propagation altering character of the photothermal lens
element and the intracavity apertures. Nonetheless, Solimini
(1966) refined the apparatus and measured the absorption
coefficients of 27 organic liquids using this method.

<Figure
1.9>

Figure 1.9 Transient
signals observed using the intracavity photothermal lens
apparatus. The top trace was obtained with an extra-cavity
pinhole and the bottom trace was obtained without the pinhole.
This data was used to confirm the premise that the laser was
operating in single mode and that the signal was generated by the
internal apertures. These signals were difficult to analyze
because of the interrelationships between laser power and cavity
losses. (Figure 2 from Gordon, et al. 1985)

The first extracavity sample
photothermal lens apparatus was used by Grabiner, et al.
(1972) to measure vibrational relaxation rate constants. Hu and
Whinnery (1973) recognized that the extracavity sample
configuration would be more flexible and could also result in
sensitive absorbance measurements. The apparatus and beam
analysis, shown in Figure 1.10, is essentially the same as that
used for single laser photothermal lens spectroscopy today. The
transient signals produced extracavity are less complicated than
those of the intracavity configuration and the theory describing
the transients is more tractable. The essential components of the
apparatus are;

the coherent, laser
excitation source which can deliver high optical powers
over a small cross-section area of the sample

a low-absorbance sample

a spatial filter or pinhole
placed in far field

a detector to measure the
power past the pinhole.

<Figure
1.10>

Figure 1.10 A schematic of
the extra-cavity photothermal lens spectrometer used by Hu and
Whinnery (1974) to measure the optical absorbances in transparent
fluids. The lens focuses the laser beam one confocal distance in
front of the sample cell. The pinhole and detector are placed in
far field of the focus. (Figure 3 from Whinnery 1974)

The extracavity photothermal lens
spectroscopy signal can be described in terms of the focal length
of the thermal lens formed within the sample. The simplest form
of the focal length is found by assuming that al<<1
and unit quantum efficiency for heat production. A sample excited
by a laser beam with an irradiance of

where E(r) (W m­2)
is the radially dependent irradiance, and F0
(W) is the incident radiant power, will produce a time-dependent
photothermal lens with a focal length, f(t),

where f(oo) (m) is the
steady-state focal length formed at infinite time

and tc
(s) is the characteristic thermal time constant

where k (J cm­1s­1K­1)
is the thermal conductivity. n0 is the
refractive index of the medium where detection takes place
(normally air), n the refractive index of the sample, T
(K) the temperature, r (kg m­3) the density, and CP
(J kg­1K­1) the specific heat. The lens
is formed because the optically heated sample has a different
refractive index from that of the bulk of the sample. The
differential term (dn/dT)P is the
temperature dependent refractive index change at constant
pressure. The shape of the temperature change produced by a
Gaussian excitation source is parabolic near the center. The
parabolic refractive index perturbation is equivalent in form to
a simple lens.

The photothermal lens signal is
obtained by monitoring the laser power that passes through a
pinhole placed far from the sample. The photothermal lens will
either focus or defocus the laser. When this happens, the power
at the center of the beam will either increase or decrease. This
change in power is maximized when the sample is placed one
confocal distance to either side of the laser's focus. In this
case the relative change in power monitored past the pinhole
aperture is

where Fd(t) is the
time-dependent power and the confocal distance is z0=n0pw02/l, w0
being the beam waist radius at the focus and l (m) is the
wavelength of the laser. The + sign applies to samples placed
before the focus, the - sign for samples behind the focus. The
time dependent signal observed past the pinhole is

Essential components to
interpreting the signal are;

the time dependent signal
increases or decreases the power past the pinhole

the time constant for signal
evolution, tc, is proportional
to the square of the beam waist radius in the sample

the signal magnitude is
proportional to the absorption coefficient, pathlength,
and excitation power

the signal magnitude also
depends on the thermal, k, and optical, (dn/dT),
properties of the sample

for times much greater than tc,
the steady-state power change is related to absorption
coefficient by

Thus the absorption coefficient
can be obtained by measuring the power change with knowledge of
the temperature dependent refractive index.

<Fig
1.11>

Figure 1.11 Illustration
of the beam geometry and definitions used for extra-cavity
photothermal lens spectroscopy. (Figure 4 from Whinnery 1974)

It is difficult to see from these
equations how photothermal lens spectroscopy method can enhance
absorbance measurements. Dovichi and Harris (1979) introduced the
concept of the enhancement factor. The enhancement factor is the
ratio of the photothermal lens signal magnitude to that which
would be obtained using conventional transmission spectroscopy.
For weakly absorbing samples, the transmission spectroscopy
signal can be cast in a form similar to that for the photothermal
lens spectroscopy signal

where Fl is the power after
passing through the sample. The ratio of the photothermal lens
signal to this signal yields the enhancement factor

The enhancement factor is a
function of the thermodynamic and optical properties of the
solvent, and on the power used to excite the sample. Nonpolar
solvents are particularly useful for trace analysis because of
their relatively high (dn/dT)P
and low k. For example, CCl4 has
temperature dependent refractive index of -6.12x10­4
K­1 and a thermal conductivity of 0.103 W m­1K­1
(Dovichi 1987). The theoretical enhancement factor is 11560 W­1
for the 514 nm line of an argon ion laser. Of course, the higher
the power, the greater the enhancement. Even a modest 10 mW laser
will yield signals that are over one hundred fold better than
those of the conventional transmission spectrophotometer.
Absorption coefficient detection limits in 1 cm cuvettes are
about 10­7 cm­1. This detection limit was
reported by Dovichi and Harris (1981a) for 514.5 nm excitation of
samples in CCl4 solvent using 160 mW of laser power.
The enhancement factor under these conditions is ~1850. Based on
these, the absorbance detection limits calculated for the
equivalent conventional transmission spectrophotometer would be
2x10­4 absorbance units. Although it is a matter for
discussion, this is about what one might expect from a double
dispersing transmission spectrophotometer.

The characteristic time constant,
tc, should also be considered in the
experimental design. With a shorter time constant, more
measurements can be made in a given time. Since replicate
measurements can be used to increase the precision of the
estimate, the shorter time constant resulting from smaller focus
spot sizes, are favored. For example, CCl4 has a
thermal diffusivity of DT=7.5x10­8
m2 s­1. A laser with a beam waist radius
of 1 mm in the sample cell will produce a signal with a
characteristic thermal time constant of 3.3 second whereas using
a 10 mm beam waist radius, tc=0.33
msec. The 10 mm beam would allow 104
replicate measurements in the same time required to obtain one
measurement with a 1 mm beam waist. The measurement precision
would increase by 100 using the smaller beam waist and equivalent
measurement times.

The first analytical application
of photothermal spectroscopy was the trace level determination of
Cu(II) with an EDTA complex reported by Dovichi and Harris
(1979). They used the single laser extracavity photothermal lens
apparatus. This method is perhaps the most well known and used of
all the photothermal spectroscopy methods. The relative
simplicity of the apparatus coupled with the low solution
absorption detection limits, 10­7 cm­1
(Dovichi and Harris 1981), make it highly attractive for trace
analysis applications.

1.5.4 Photothermal
interferometry

Shortly after the discovery of
the photothermal lens effect, researchers found that the
photothermal induced refractive index change could be measured by
more direct means. McLean, Sica, and Glass (1968), and Longaker
and Litvak (1969) recognized that optical absorption resulting in
sample heating and subsequent changes in refractive index would
cause a phase shift in light passing through the heated region.
The optical phase shift can be detected with an interferometer.
The method of using optical interferometry to measure refractive
index changes was not in itself new, but using an excitation
laser to heat the sample while monitoring the refractive index
change was. Most photothermal interferometry apparatuses are
based on laser excitation sources. Stone (1972, 1973) showed that
both coherent and wide-band incoherent sources could be used.
Stone used the modified Jamin interferometer apparatus shown in
Figure 1.12 to obtain the absorption spectrum of chlorobenzene
shown in Figure 1.13. Using this apparatus, 2-3 mW of excitation
source power could be used to measure absorption coefficient of
about 2x10­5 cm­1.

<Figure
1.12>

Figure 1.12 Modified Jamin
interferometer apparatus used by Stone (1973). Incoherent light
from a xenon arc is collimated and filtered by a series of
band-pass filters before passage through the center of the sample
cell along (c). Helium-neon laser light detects the optical phase
shift. The laser light is split by the optical flat and passes
through a reference path (a) and a probe path (b). The two laser
beams are combined at the second optical flat. One detector
monitors the power of the reference beam and the other the power
in the interfering beams (a+b). A phase shift in the two
interfering beams results in a power change at the signal
detector. Phase shifts are found from the ratio of the signal to
reference powers. (From Whinnery 1974, Figure 7)

<Figure
1.13>

Figure 1.13 Data obtained
for chlorobenzene using the photothermal interferometer of Figure
1.12 (solid), and that of bromobenzene in a glass capillary
(broken line) obtained with a transmission spectrophotometer. The
structured absorption features are C-H stretch vibrational
overtones.

The conventional approach to
measuring small absorption coefficients is to increase the
optical pathlength. The data in Figure 1.13 compares results
obtained using long pathlength transmission spectrophotometry to
those of the photothermal interferometer. Transmission losses may
be due to reflection, scattering, and absorption. The finite
transmission losses seen in the bromobenzene spectrum are not
necessarily due to optical absorption. On the other hand, the
photothermal interferometer responds only to absorption. The
resulting spectrum is technically an excitation spectrum since
the heat is generated by optical absorption of the excitation
light.

An almost astonishing feature of
the interferometry method is its sensitivity. Davis and
Petuchowski (1981) have measured absorption coefficient detection
limits as low as 10­10 cm­1 for gaseous
samples in windowless absorption cells using chopped infrared
excitation lasers at irradiances of 2.5 MW m­2. Other
sensitive interferometry methods for measuring the photothermal
effect are discussed by Friedrich (1983), and Dovichi (1987) has
reviewed the applications to chemical analysis.

The interferometry studies of
Longaker and Litvak (1969) used cameras to obtain images of phase
shift patterns resulting from the refractive index perturbation
produced by pulsed Nd glass laser sample excitation. This classic
and innovative work revealed a wealth of information regarding
photothermal effects. The apparatus used for these studies in
shown in Figure 1.14. The photographic camera was used to obtain
pictures of the fringe patterns for visual analysis and the
vidicon camera was used to obtain quantitative information for
critical evaluation of the data. Photographic images shown in
Figure 1.15 reveals some of effects they observed. For absorbing
samples, the refractive index perturbation had two components
with different space and time behaviors. A long-lived transient
was observed near the region excited by the pulsed laser. This
component was the thermal perturbation produced by the
photothermal effect.

<Figure
1.14>

Figure 1.14 Interferometer
used by Longaker and Litvak (1969) to obtain images of the
density perturbation in gas and liquid samples. The pulsed Nd
laser is used to excite the sample and the continuous Ar+
laser is used to probe the refractive index changes. The camera
records the fringe shift of the Ar+ laser beam.

<Figure
1.15>

Figure 1.15 Image data
obtained with the apparatus illustrated in Figure 1.14. The
picture on the left is that of a 5 cm sample of non-absorbing
liquid CS2. No thermal perturbation is observed and
the fringe shift is due only to the acoustic wave generated by
electrostriction. The image on the right is for a weakly
absorbing sample and has both a thermal perturbation (in the
center) and an acoustic wave component (the dark ring). (Figure
11 from Longaker and Litvak, 1969)

The phase shift, df (rad),
produced from the thermal component is related to the density
change through

were l is the wavelength of the laser used to
measure the refractive index change. The theory developed by
Longaker and Litvak predicts that for weakly absorbing samples
with rapid excitation and excited state relaxation times, the
on-axis time dependent density change for pulsed radiation is

for times much shorter than tc.
Thus the signal rise-time is limited by the same acoustic
relaxation time that limits the signal magnitude in photoacoustic
spectroscopy. The spatial density change could be quantitatively
determined by counting interference fringes. Vidicon camera data
were analyzed in terms of the thermal-induced phase shifts and
the focal length of the photothermal lens resulting from the
thermal perturbation. This later data was found to agree with the
theory developed by Gordon, et al., to describe the
photothermal lens.

In addition to the thermal
component, a short-lived transient component was found. This
component propagated away from the heated region as a wave. This
was identified as an acoustic pressure wave. Referring to the
ammonia gas data in Figure 1.15, the thermal perturbation can be
seen at the center and the dark ring around the central
perturbation is due to the propagating pressure or acoustic wave.
The acoustic wave is produced by the rapidly expanding sample
heated by the pulsed laser. The ammonia gas absorbs energy from
the pulsed excitation source. Excited state ammonia rapidly
relaxes hereby increasing the temperature of the sample. The
heated sample then expands to produce an acoustic compression
wave. The compression wave propagates out away from the excited
region. The compression increases the density of the gas thereby
causing an increase in the refractive index. Thus the acoustic
wave also results in a photothermal signal. Although the acoustic
wave carries away some of the energy, most of the thermal energy
remains in the region local to the excitation laser irradiation
(Bialkowski 1988). Although Longaker and Litvak were not the
first to observe this effect, their pictorial observations
clearly demonstrate the principles of photothermal and
photoacoustic spectroscopies and showed the connection between
the two.

Photoacoustic wave generation by
the photothermal effect is only one of several mechanisms for
acoustic wave generation. Figure 1.15 also shows data obtained
for CS2, a non-absorbing, highly polarizable liquid.
The CS2 data illustrates acoustic waves created
without a photothermal perturbation. The acoustic waves are
generated by an effect called electrostriction wherein
polarizable media are compressed by the electric field of the
optical radiation. Electrostriction has not, to date, been
observed using photothermal spectroscopy methods.

1.5.5 Two-laser photothermal
lens spectroscopy

The two-laser photothermal lens
apparatus was used before the extracavity single laser method was
found. Grabiner, et al. (1972) used a helium-neon laser to
probe the photothermal lens produced by a pulsed, infrared laser.
They used this two-laser photothermal lens apparatus to determine
the vibrational relaxation rate constants for methyl chloride and
methyl fluoride gases. Later, Siebert, et al. (1974) used
the technique to study relaxation of vibrationally excited CD4,
SO2, and OCS. Of interest was the rise-time of the
photothermal lens signal. The rise-times were measured as a
function of added gas pressure and the vibrational relaxation
rate constants were deduced from these measurements. The
technique was found to be quite satisfactory for relaxation times
that were greater than the acoustic limited rise-times. The
vibrational relaxation rate constants compared well to those
obtained using other methods. Although not exploited in this
work, Grabiner, et al. and Siebert, et al. showed
that by using this photothermal lens method, infrared absorption
could be measured using visible detectors. This would later be
used to the advantage of short pathlength infrared absorption
studies.

Long, et al. (1976) used
the two-laser photothermal lens apparatus shown in Figure 1.16 to
measure absorption spectra due to vibrational overtones in pure
solvents. A repetitively chopped continuous dye laser was used to
form the photothermal lens in the sample and a continuous
helium-neon laser probed the resulting lens element. The
equations that describe the temperature change and focal length
of the photothermal lens are the sample as those given above.
However, several advantages to using separate excitation and
probe light sources in photothermal lens spectroscopy can be
realized in this configuration;

The dye laser can be scanned
to produce excitation spectra of the sample without
having to account for photodetector wavelength response.

The excitation source can be
focused directly into the sample. This increases the
irradiance and the resulting photothermal lens signal by
decreasing the beam waist radius in the sample.

A lock-in amplifier can be
used to decrease the bandwidth of the measurement thereby
enhancing the signal to noise ratio.

<Figure
1.16>

Figure 1.16 A dual-beam
photothermal lens spectrometer. The dye laser excites the sample
and the probe source monitors the resulting refractive index
change through the photothermal lens effect. The diverging probe
beam passes through a pinhole spatial filter to develop the
signal. The wavelength filter rejects the excitation wavelength.
The chopped signal is processed with a lock-in amplifier to
improve the signal to noise ratio. The dye laser can be scanned
to obtain photothermal excitation spectra. (From Fang and
Swofford 1987, Figure 6)

Twarowski and Kliger (1977a)
developed a quantitative theory to describe the pulsed laser
excited photothermal lens spectroscopy signals and applied this
theory to study the two-photon absorption of benzene (1977b).
This was the first derivation of the time dependent thermal lens
given for pulsed laser excitation. Basically, a pulsed laser with
an integrated irradiance H(r,t) (J m­2)
of

will produce a temperature change
of

for a single-photon absorption
process and for times greater than required for acoustic
relaxation. The inverse focal length was found to be

The main characteristics of the
pulsed laser photothermal lens spectroscopy signal are;

the signal magnitude is
greatest at zero time, just after acoustic relaxation of
the sample. This allow the pulsed laser technique to be
used to study excited state relaxation kinetics.

As with the chopped
continuous excitation laser method, the pulsed laser
method can use dye lasers to obtain excitation spectra
and the excitation laser can be focused into the sample
cell resulting in greater signal magnitudes.

The high irradiance at the
focus can be high enough to induce nonlinear absorption
effects. The multiphoton absorption signal is essentially
the same but with the caveat that the absorbed energy is
proportional to the integrated irradiance raised to the
power of the number of photons absorbed. Thus the
effective squared beam waist radius is decrease by a
factor inversely proportional to the number of photons
absorbed per transition, w2/p w2.
This further enhances the signal magnitude and has lead
to the belief that photothermal lens spectroscopy is very
useful for multiphoton spectroscopy.

Barker and Rothem (1982) pointed
out that the simple theoretical description of the photothermal
lens shown above does not yield quantitative results in the early
times of the signal. They point out an apparent dilemma wherein
Grabiner, et al. (1972) use an acoustic wave equation to
model results while Twarowski and Kliger (1977a) use a thermal
diffusion equation. Barker and Rothem developed a quantitative
theory for predicting the photothermal lens signal that takes
into account several hydrodynamic relaxation effects. This theory
predicts that all but the first of the five points given above
hold, but that the signal rise-time is limited by the rate at
which the density can change. The latter is related to the sound
velocity and the radius of the excitation source (Barker and
Toselli 1989).

Fang and Swofford (1983) have
written an excellent overview of the theory and developments in
photothermal lensing spectroscopy. Dovichi (1987) has reviewed
the literature and has commented on analytical applications of
the technique. Absorbance detection limits of about 10­7-10­8
cm­1 for liquids and gases using 10-200 mW continuous
sources. Sell (1989) has collected together a number of chapters
addressing many important applications of photothermal
spectroscopy. Morris and Fotiou (1989) have reviewed applications
to chromatography detection. Dovichi (1990) has included this
technique in his review of laser-based micro-analysis.

1.5.6 Photothermal deflection,
refraction, and diffraction

The mirage is a common and well
understood example of the photothermal effect. However, the
analytical method based on this principle, photothermal
deflection spectroscopy, was somehow overlooked until Boccara, et
al. demonstrated probe laser beam deflection in 1979. The
method was applied to surface analysis. A typical experimental
set up for photothermal deflection analysis of surfaces is shown
in Figure 1.17c. Like the indirect photoacoustic spectroscopy
method, this method may be used to examine optical absorption at
or near the surface of solid samples. The sample absorbs optical
radiation and heats the gas or liquid above the surface. The
heated gas acts like a prism and deflects the probe laser
incident tangent to the surface. Probe laser beam deflection is
monitored with a position sensing detector. The apparatus is very
easy to set up and can produce very sensitive measurements of
surface absorption.

The theory for describing the
photothermal deflection signal has been worked out for both
chopped and pulsed excitation sources. This theory is more
complicated than that describing homogeneous fluids because the
thermal conduction in the solid and the fluid must both be
accounted for. The temperature change that occurs upon pulsed
irradiation of a surface with an adsorbed absorbing species is

where the x direction is
normal to the surface, kS is the unitless
surface absorption coefficient, and DT
and rCP are the
thermal diffusivities and heat capacities of the solid (s)
and fluid coupling medium (f) respectively. The deflection
angle of a probe being refracted by the temperature gradient
produced by the heated surface is

The deflection angle is monitored
using a position sensing detector which is placed a short
distance from the surface. A change in angle at the sample
results in a displacement of the probe laser spot on the
detector. For small angles, the linear displacement of the probe
laser beam spot is directly proportional to the deflection angle.
The above equation shows that the magnitude of the signal will be
a function of the offset, x, of the probe laser beam from
the surface. There is an optimum offset for maximum signal. This
optimum offset is a function of time. The time is that required
for the temperature change to diffuse to the region probed by the
laser. The temperature diffusion process is often called the
thermal wave. This equation also shows that at a particular
offset, the time-dependent deflection signal will rise and then
fall with time. The time to the maximum is tmax=x2/6DT,f.
So the time to the maximum signal and the magnitude of the
maximum signal are both functions of the displacement of the
probe laser beam relative to the surface. This distance is
difficult to measure and so photothermal deflection cannot be
used to measure absolute absorption coefficients.

One application of this technique
caught on rapidly. It was apparent that photothermal deflection
could be used for topographic and thermal characterization of
samples. The signal magnitude depends on the surface topography,
surface absorption coefficient, the thermal properties of the
fluid, and the thermal properties of the solid. All other
parameters being equal, the signal dependence on the surface to
probe laser beam offset allows the surface topography to be
measured. For relatively flat surfaces, signal dependence on the
solid's thermodynamic parameters allows a thermal image of
the solid to be obtained (Murphy and Aamodt 1980, 1981). A solid
with a constant surface absorption or an optically dense solid
will result in a signal that is inversely proportional to the
solid's thermal conductivity. An example of a thermal imaging
apparatus is shown in Figure 1.18. When the solid sample is
raster scanned under a focused excitation laser source, the
photothermal deflection signal magnitude will be inversely
proportional to the solid's thermal parameters. This thermal
imaging technique has been used to determine sample thickness,
inclusions in metals (McDonald 1986), inspect coatings (Busse
1989), and imaging boundaries at crystal domains (Murphy, et
al. 1986). The thermal image shown in Figure 1.19 is of
aluminum metal. The lighter regions are thought to be due to
subsurface inclusions in the metal. Several applications of
photothermal deflection spectroscopy have been discussed in the
recent chapter by Fournier and Boccara (1988).

<Figure
1.18>

Figure 1.18 Photothermal
deflection apparatus used to measure the photothermal image of a
surface. The magnitude and phase of the photothermal deflection
signal is measured at each position of sample excitation. The
sample is raster scanned using the x-y translational stage. The
microcomputer records the data and performs image analysis.
(Figure 4 from Murphy, et al. 1986)

An useful extension of this
technique is to irradiate the entire surface with a series of
patterns instead of scanning the excitation and probe lasers
across the surface. Fotiou and Morris (1986) use a moving
Hadamard encoded mask to analyze the spatial distribution of
absorption on stationary thin-layer-chromatography plates. This
method is more fully described in Morris and Fotiou (1989). A
typical apparatus is shown in Figure 1.20. This apparatus was
used to measure band positions and absorptions on dyed plates.
Imaging thus far has been one dimensional but there is no
apparent reason why two-dimensional images could not be obtained.

<Figure
1.20>

Figure 1.20 One
dimensional imaging apparatus developed for plate chromatography
based on a time-multiplexed Hadamard encoded mask. Each position
of the mask results in a unique surface excitation pattern. A
photothermal deflection signal is recorded for each position of
the mask and the resulting data set is transformed. The
transformed data yields the absorption image of the thin layer
chromatography plate. (Figure 11 of Morris and Fotiou 1989)

Jackson, et al. (1980,
1981) extended the photothermal deflection method to include
optically transmitting gas and liquid analysis. In these
experiments the excitation and probe lasers propagate collinear
through the sample cell. In this case the pulsed laser induced
temperature change results in the deflection of a collinear probe
beam

There is a subtle distinction
between the photothermal methods used for surface and transparent
sample analysis. For surface analysis, the probe laser is used to
detect a refractive index gradient formed in the media above the
surface. In transparent samples, the refractive index is changed
within the sample itself. Thus the deflection angle signal is
essentially the same as the pulsed laser photothermal lens
inverse focal length. In fact, the signal strengths observed are
about the same (Jackson, et al., 1981). This method is
very similar to photothermal lens spectroscopy. The similarity
between the photothermal lens method and the beam deflection
technique has been noticed by many authors, for example see Tam
(1983, 1986, 1989) and Dovichi (1987). Photothermal lens and
photothermal deflection methods both rely on the generation of a
refractive index gradient in the sample itself. Collectively,
they have become known as refractive index gradient detection or
photothermal refraction spectroscopy methods (Zharov and Letokhov
1986, Tam 1986). The different geometries for sample excitation
and monitoring of the photothermal response are shown in Figure
1.17.

The main advantage of
photothermal deflection spectroscopy is in the versatility. The
same method can be used for solid, surface, liquid, and gas phase
analysis. Excitation sources can be either pulsed or chopped
continuous. The absorption coefficient detection limits for these
methods are about the same as those of the two-laser photothermal
lens method. Fournier, et al. (1980) demonstrated
absorption coefficient detection limits of 10­7 cm­1
for gas phase samples in a windowless flow cell using a 1 W
modulated infrared carbon dioxide excitation laser. Long and
Bialkowski (1985) used a 10 mJ pulsed infrared laser to obtain
gas phase absorption coefficient detection limits equivalent to
10­8 cm­1. Bialkowski and He (1988) later
used an etalon to amplify the deflection angle signal and found a
100 fold signal-to-noise ratio improvement, or ~10­10
cm­1 detection limit for a 10 mJ pulse. Jackson, et
al. (1981) demonstrated 10­6 cm­1
absorption coefficient detection of benzene in CCl4
using a 1 mJ pulsed dye laser. The solvent itself had an
absorption coefficient of 10­6 cm­1 and
absorption due to the benzene analyte was found by scanning the
wavelength of the pulsed pump laser. The estimated limit of
absorption coefficient detection was 10­7 cm­1.
Dovichi (1987) pointed out that the photothermal refraction
methods are advantageous when there is a significant signal due
to sample cell window absorbance. Since the excitation and probe
lasers do not have to pass into the sample at the same spot,
photothermal perturbations due to the window can be ignored.
There has been several reviews on probe beam deflection
techniques. These reviews are often compiled along with those for
photoacoustic spectroscopy. The reviews by Tam (1983, 1986,
1988), Murphy, et al. (1986), Dovichi (1987), Fournier and
Boccara (1988) all cover aspects of this method. The books edited
by Mandelis (1987) and Hess (1989a, 1989b) have chapters devoted
to this method.

Another method based on the
generation of refractive index changes within the sample is
photothermal diffraction spectroscopy. Laser-induced gratings
have been known for quite some time (Eichler, et al. 1986)
and are the basis of optical holography (Collier, et al.
1971). However, the first analytical application was by
Pelletier, et al. (1982), who demonstrated that a
refractive index grating could be formed in a weakly absorbing
sample by interfering two beams from a single excitation laser
within the sample. The apparatus is shown in Figure 1.21. The
grating diffracts a probe laser beam at a specific angle that
satisfies the Bragg condition.

<Figure 1.21
>

Figure 1.21 A
schematic of an apparatus used for photothermal diffraction. The
two excitation beams are mutually coherent, arising from the same
laser excitation source. Interference of the two beams produced a
periodic irradiance and subsequently a periodic refractive index
perturbation, or phase grating, in a weakly absorbing sample. The
phase grating is probed with a second probe laser. (Figure 2 of
Pelletier, et. al 1982)

For pulsed laser
excitation, the diffracted probe beam power is (Pelletier and
Harris 1983)

Here F+ is the diffracted and F0
is the incident probe laser power, Q is the total
(combined) pulse energy, l is the wavelength of the probe laser, and
2q
is the angle between the two pulsed pump laser beams. The
diffraction signal is proportional to (aQ)2, thus apparently
limiting the sensitivity at low concentrations. However, unlike
infrared emission, the background is very small. The background
noise limitation is essentially the same as those of laser
excited fluorescence spectroscopy. Current absorbance detection
limits are about ~10­6 cm­1. Although not
exploited to any great extent, this method has potential for
trace analysis. The main advantage of this technique is
apparently in the relatively simple data that result when the
sample undergoes nonlinear absorption. In this case the distorted
grating formed by nonlinear absorption can be decomposed by
Fourier analysis into a series of orthogonal gratings, each with
a different spatial period. Each grating then produces a
different diffraction angle. The type of nonlinear absorption can
be determined by analysis of the magnitude and irradiance
dependence of the probe laser at each diffraction angle. The
connection between photothermal lens, photothermal refraction,
and photothermal diffraction spectroscopies has recently been
given by Harris (1986) and the principles and applications of the
photothermal diffraction method have recently been reviewed by
Zhu, McGraw, and Harris (1992).

1.5.7 Photothermal radiometry

Another photothermal method is
photothermal radiometry. In photothermal radiometry, the sample
is excited with an optical source and the infrared emission is
monitored. The infrared emission is related to the sample
temperature by the black-body radiation law (Ingle and Crouch
1988)

where B(l,T) (W
sr­1m­2) is the radiant emissivity, h
(J s) is Planck's constant, k (J K­1) is
Boltzmann's constant, and e(l) is the sample emissivity. For samples at
thermal equilibrium, a(l)=e(l). The relative change in spectral
radiance with respect to temperature is

In the mid-infrared region, hc/lkT<1
and for pulsed laser excitation

where lem is the emission
wavelength and lex is the excitation
wavelength. The important features of this equation are;

since a(lem)
and a(lex) are both
proportional to number density or concentration, the
relative emission signal decreases as the square of the
number density

The later suggests that this
method will not be as sensitive as other photothermal techniques
since the sensitivity decreases with decreasing a.

This method of analysis has a
long and somewhat obscured history. The advent of lasers and
cryogenic infrared detectors resulted in several studies of
infrared emission from excited gas samples. The method used to
study gas samples is called laser-induced fluorescence (Hocker, et
al. 1966, Yardley and Moore 1966, Stephenson, Wood, and Moore
1968, to name a few). These pioneering studies used pulsed
infrared lasers to excite specific vibrational modes while
monitoring infrared fluorescence at wavelengths different from
that used for excitation. Time resolved fluorescence emission
studies were performed to reveal the excited state vibrational
lifetimes of the low pressure gas species. These lifetimes are a
direct measure of the thermalization time of the sample. With the
notable exception of the work by Belz, et al. (1987)
infrared emission methods have been neglected for gas analysis
although the utility is apparent.

Photothermal radiometry has been
recognized as an important tool for surface studies and material
analysis (Nordal and Kanstad 1979). The solid being analyzed is
treated as a black-body emitter. The total surface emission will
follow the Stefan-Boltzmann law. The relative temperature
dependent change in surface emittance, e.g., integrating
over wavelength, is simply,

where M(T) (W m­2)
is the temperature dependent emittance of the surface and dT is
induced by the photothermal effect. The temperature change can be
produced by either pulsed or chopped excitation sources. This
method is not very sensitive and rather large temperature changes
have to be induced in the samples to obtain good thermal images.
The thermal images are not a function of surface topography
(unless three-dimensional imaging optics are used) The images
will only depend on the optical absorption coefficient and the
heat capacity of the sample. Time or phase dependent analysis of
the emittance yields information regarding the thermal
conductivity. If the integrated emission data is not processed as
indicated in the above equation, the thermal image will also be a
function of the topographical emissivity of the material. Tam
(1985) has examined the use of photothermal radiometry for solid
sample analysis and has reviewed the literature regarding
applications of the method (Tam 1983, 1986, 1989). Busse (1989)
has reviewed this in reviews of nondestructive materials
evaluation using photothermal methods.

Table 1.3 Major developments
in the early history of photothermal spectroscopy

The important discoveries in the
history of photothermal spectroscopy are given in Table 1.3. Many
of these discoveries were made possible by using lasers. Although
lasers do not have to be used to excite samples, the signals
thereby obtained are much greater than those obtained using
incoherent light sources. Historically, the birth of high
sensitivity photoacoustic and photothermal spectroscopies can be
traced back to the laser. The first application of the
photoacoustic effect was that of A. G. Bell (1880) while chemical
analysis applications of photoacoustic spectroscopy can be traced
back to Viengerov (1938). The first photothermal method was
discovered by Leite, et al. (1964) when they found an
intracavity sample, laser based apparatus gave rise to
photothermal blooming, the photothermal lens. Some time later
Kreuzer (1971) showed that photoacoustic spectroscopy could be
used for sensitive analysis when laser light sources were
utilized.

The reasons why lasers have made
such an impact on high sensitivity spectroscopy are because they
posses a high spectral brightness and they have outputs which are
coherent. The high spectral brightness allows high powers or
energies to be imparted to the sample. The coherence, in
particular the spatial coherence, allows this power or energy to
be delivered to small volumes. The signals in both photoacoustic
and photothermal spectroscopies are enhanced with smaller
excitation volumes.

1.6 Some important features of
photothermal spectroscopy

We have now come to regard
photothermal spectroscopy as a group of high sensitivity
techniques that can be used for chemical and materials analysis.
Photothermal signals arise from optical absorption in a sample.
However, photothermal spectroscopy techniques have sensitivities
far exceeding those of conventional absorption spectrophotometry.
The reasons for the high sensitivity of photothermal spectroscopy
is that it is an indirect technique for measuring optic
absorption. For an analyte with less than unit fluorescence
quantum yield, electromagnetic energy absorbed and not lost by
subsequent emission results in an increase in the energy of the
sample. Energy absorbed and not subsequently lost by emission is
usually randomized resulting in sample heating. The photothermal
spectroscopy signal is derived from this heating.

There are a variety of methods
used to monitor sample heating. Calorimetric or thermometric
methods use temperature transducers to measure sample
temperature. The method of photoacoustic spectroscopy uses a
pressure transducer to monitor the pressure wave associated with
rapid sample heating. Photothermal emission radiometry uses
photometric transducers to monitor changes in the samples
infrared emission associated with heating. Photothermal
interferometry, photothermal deflection, photothermal lensing,
and photothermal diffraction spectrometries are all photothermal
techniques that are based on monitoring refractive index changes
associated with sample heating.

The distinctions between all but
the calorimetric and photothermal radiometry techniques are
lessening. The connection between photothermal and photoacoustic
spectroscopies is apparent. Signals attributable to the
photoacoustic effect are seen in photothermal spectroscopy
experiments though the converse is not true. A pressure
transducer placed far from the excitation source will not respond
to the thermal perturbation. Photoacoustic spectroscopy
apparatuses may use probe lasers to detect the acoustic wave.
This eliminates the use of pressure transducers that may have low
response times. However, photoacoustic deflection spectroscopy is
orders of magnitude less sensitive than photothermal lensing or
deflection.

Accurate theories for describing
photothermal spectroscopy signals have been developed. In most
cases, these theories take into account the thermodynamics,
hydrodynamics, and optics of the experimental apparatuses. In
some cases, for example in the single laser photothermal lens
apparatus, the absorption coefficient may be obtained directly
from the signal if the thermodynamic and optical parameters are
known well enough. In most other cases the signal magnitude has
an instrumental factor that must be determined using samples of
known absorbance in sample matrices that are identical to those
of the unknown sample.

Background absorption
typical of water vapor at 10 mm, solvent overtones in liquids,
and impurities in fused silica in the visible

A summary of the best absorption
coefficient detection limits for photothermal and photoacoustic
methods are given in Table 1.4. The detection limits are given in
inverse energy or power units since all photothermal methods
scale proportional to the excitation. For continuous excitation,
lock-in amplifier signal processing is generally used to recover
the oscillatory signal. The noise power is proportional to the
bandwidth of the measurement, these detection limits are
inversely proportional to the square root measurement bandwidth.
The theoretical detection limits are based on thermodynamic
fluctuations in sample pressure (Slatkine 1981). The noise
equivalent power, NEP (W Hz­1/2), is

where k is the Boltzmann
constant, f is the frequency, df is the measurement bandwidth, r
and l are the radius and length of the sample cell.

The fluctuations that ultimately
limit photoacoustic spectroscopy should also place a lower bound
on photothermal spectroscopy since pressure and density are
related

where KT
(Pa­1) is the isothermal compressibility.

For gas and solution phase
analysis, photothermal and photoacoustic spectroscopy apparatuses
have been developed which yield signals that are close (1-2
orders of magnitude) to the theoretical limits of absorbance
detection. Quantitative work in solid analysis is nearly
impossible because of the difficulty in preparing standard
samples. These detection limits are lower than the background
absorbance of water and other trace gases in the atmosphere, and
of solvents used to host the analytes. The lower detection limits
are obtained for gas samples because of reduced matrix
absorptions and favorable thermodynamic parameters. The problem
with the sensitive absorbance measurement methods is not so much
the measurement of low absorption coefficients, but rather in
discriminating the low analyte from that of the solvent or other
species in the sample.

From these and other examples it
is clear that photothermal spectroscopy is a valuable tool which
can be used to solve a variety of chemical and materials analysis
problems. Some salient features are;

The sensitivity of
photothermal spectroscopy is theoretically enhanced over
that of conventional absorption spectrophotometry. This
theoretical enhancement has been realized and absorbance
detection limits of ~10­7 in liquids and ~10­10
in gases are possible. High sensitivity has allowed the
measurement of weak optical absorbances in pure samples
and trace analysis, and in volume restricted samples.

Photothermal signals are
inversely proportional to the excitation volume. This
arises not only because of the higher temperature changes
that can be induced with a given power or energy, but
also because photothermal signals are usually derived
from a spatial gradient in the resulting refractive index
change. The small volume character of photothermal
spectroscopy has lead to its use for micro-analysis and
effluent detection in chromatography.